Number Theory Algorithms

Perform Number Theory algorithms & arithmetic operations for very big numbers

Calculator:

Add two big integer numbers

Subtract two big integer numbers

Multiply two big integer numbers

Divide two big integer numbers

Power of a big integer number

Root of a big integer number

Greatest Common Divisor (GCD) of two big integer numbers

Lowest Common Multiple (LCM) of two big integer numbers

Module of two big integer numbers

Module Inverse of two big integer numbers

Module Power

Check if a big integer is prime

Euler's phi-function

Factorial

Next prime to a big integer number

Next twin prime pair to a big integer number

Algorithms:

Simple Quadratic Form. Solve for x,y such that bxy+dx+ey=f where b,d,e,f,x,y in Z.

Euclidean Algorithm. Compute the Greatest Common Divisor (GCD) of two numbers a and b.

Extended Euclidean Algorithm. Solve for x, y such that ax + by = gcd(a, b).

Linear Diophantine Equation In Two Variables. Solve for x,y such that ax+by=c.

Linear Congruence In One Variable. Solve for x a congruence of the form ax ≡ b (mod m).

Linear Congruence In Two Variables. Solve for x,y, a congruence of the form ax+by ≡ c (mod m).

Tonelli-Shanks Algorithm. Calculate the Quadratic Residue Modulo. Solve for x, a congruence of the form x² ≡ a (mod p) where p is prime.

Mod Factors. Calculate modular possible factors for a given number and a modulus. Find n ≡ bc (mod a) where (ax + c)(ay + b) = a(axy + bx + cy) + bc = n.

Primes List. List of primes ordered in columns.

Note: Performance is based on the device.